Influence Of Heel On Yacht Sailplan Performance - hiper 08

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Influence Of Heel On Yacht Sailplan Performance - hiper 08 Powered By Docstoc

           Fabio Fossati, Full Professor, Wind Tunnel - Politecnico di Milano, Italy,
           Sara Muggiasca, Researcher, Department of Mechanical Engineering, Politecnico di Milano, Italy


This paper presents research activities carried out by the authors to investigate the influence of heel on yacht sailplan
performance by means of wind tunnel test techniques and CFD numerical simulations. Main results concerning wind
tunnel testing activities carried out in the Politecnico di Milano Twisted Flow Wind Tunnel investigating the upwind
performance of sails both heeled and upright are presented. Finally the heeled plane approach which is largely used in the
aerodynamic models available up to-date for VPP use is outlined and discussed

 1. INTRODUCTION                                                      available up to-date for VPP use is outlined and
Sailing yacht heeling effect on sails aerodynamics
represents one of the tougher issue of upwind                         2. TWISTED FLOW WIND TUNNEL
aerodynamics ([1] [3] [6] [7]) and some discussions have
been recently found in literature] [8]. In fact this is a very        With the purpose of supporting, with a state of the art
complex topic with strong implications for                            facility, the world-wide recognised excellence of
methodologies to compute sailboat aerodynamics for                    Politecnico di Milano research in the field Wind
Velocity Prediction Program design tool.                              Engineering as well as general Aerodynamics,
This paper deals with research activities carried out at              Politecnico di Milano decided to design and build a new
Politecnico di Milano Twisted Flow Wind Tunnel in                     large wind tunnel having a very wide spectrum of
order to investigate the performance of upwind sails in               applications and very high standards of flow quality and
heeled condition. This work is a part of an overall and               testing facilities. The Wind Tunnel has been fully
comprehensive general research program started in 2005                operative since September 2001 and from the first year of
with partial funding from the ORC with the aim to                     operations has been booked for sailing yacht design
investigate a series of rig planform variations in mainsail           applications.
roach and jib overlap in order to overcome some                       Figure 1 shows an overview of the P.d.M. facility: it’s a
perceived inequities in the ratings of boats of various rig           closed circuit facility in a vertical arrangement having
design racing under the International Measurement                     two test sections, a 4 x 4m high speed low turbulence and
System (IMS).                                                         a 14 x 4m low speed boundary layer test section.
The results of this investigation are used to assist the              A peculiarity of the facility is the presence of two test
International Technical Committee (ITC) in changing the               sections of very different characteristics, offering a very
formulations in the ORC INTERNATIONAL VPP sail                        wide spectrum of flow conditions, from very low
aerodynamic model.                                                    turbulence and high speed in the contracted 4 x 4m
This paper in the first part presents test arrangements,              section (Iu<0.15%, Vmax=55 m/s), to earth boundary
procedures and methodologies that have been carried out               layer simulation in the large wind engineering test
both for systematic gathering of wind tunnel data and                 section.
subsequent analysis in order to describe aerodynamic                  With reference to yacht sails aerodynamic studies, they
behaviour of different sailplans both in upright and                  are performed in the boundary layer test section which
heeled condition. Some interesting experimental results               allows for testing large scale models (typically 1:10 -1:12
and trends are presented and discussed.                               for IACC yacht model) with low blockage effects at
Differences of sail performance at different heel                     maximum speed of 15 m/s.
configurations outlined by means of wind tunnel test                  A very important peculiarity concerning yacht
results are clarified with the aid of numerical results               aerodynamics is that since the wind speed increases with
obtained using RANS methods performed on the tested                   height due to the boundary layer phenomena and the boat
sailplan configurations. For this reason, during the tests            speed is constant, this means that the apparent wind
authors gave special attention to measure also sails flying           speed incident onto a yacht also increases with height
shapes in order to provide sails geometry useful for CFD              and, in addition, its direction changes, rotating away
purposes.                                                             from the yacht’s heading with increased height.
Paper presents also a detailed description of methods and             This is a very important topic in wind tunnel testing on
techniques used by the authors in order to detect sails               sailing yacht scale models, that has to be carefully
shapes.                                                               considered, because the forces developed by the sail plan
Finally the so called “heeled plane approach” [3], [6], [7]           are due to the apparent wind incident onto the sails and
which is largely used in the aerodynamic models

the sail shape and trim is strongly related to the apparent     techniques, the model can be rigged using standard
wind profile.                                                   model yacht fittings and small dinghy fittings without
Therefore, for proper similitude modelling, the apparent        any additional work becoming too small to handle,
wind velocity shear and twist profile has to be                 commercially available model yacht sheet winches can
reproduced in the wind tunnel for testing stationary            be used and, most important, deck layout can be
models.                                                         reproduced around the sheet winch, allowing all the sails
                                                                to be trimmed as in real life.

Figure 1. Politecnico di Milano Wind Tunnel
While the variation in wind speed with height can be
modelled in the wind tunnel using similar procedures as         Figure 2. Twisted Flow Devices
for conventional wind engineering testing, the twisted          Moreover the model yacht drum type sheets are operated
flow is a more difficult task to deal with for a stationary     through a 7 channel proportional radio control system,
wind tunnel yacht model, because the true and apparent          except that the aerial is replaced by a hard wire link and
wind speeds are coincident.                                     the usual joystick transmitter is replaced by a console
At this purpose the so called Twisted Vanes Device has          with a 7 multi-turn control knobs that allow winch drum
been designed: the basic idea of the design process is to       positions to be recorded and re-established if necessary.
generate a large-scale vortex with its spin axis aligned        The sheet trims are controlled by the sail trimmer who
with the wind tunnel steady state flow direction, resulting     operates from the wind tunnel control room.
in a twisted flow area corresponding to the model               Figs. 3 show a typical model mounted in the wind tunnel.
Moreover, basic design requests were the following:

•    easy to adjust
•    easy to install/remove
•    economical solution both in terms of first
     installation and running costs

The originality of the Politecnico di Milano Twisted
Flow Device compared to the other solutions [4] is the
central positioning of the device, not occupying the entire
tunnel section. In fact, the role of the Twisted Flow
                                                                Figure 3. Yacht model in the boundary layer test section
Device is just to turn left the lower part and to turn right
the upper part of the flow. The side flow not passing           A high performance strain gage dynamic conditioning
though the vanes is allowed to move vertically balancing        system is used for balance signal conditioning purposes.
the flow rate.                                                  The balance is placed inside the yacht hull in such a way
Fig. 2 shows the Twisted Flow Device in the tunnel              that X axis is always aligned with the yacht longitudinal
boundary test section.                                          axis while the model can be heeled with respect to the
A complete model, consisting of yacht hull body (above          balance.
the waterline) with deck, mast, rigging and sails is            The wind tunnel is operated at a constant speed after the
mounted on a six component balance, which is fitted on          wind speed profile and wind twist have been properly
the turntable of the wind tunnel (fig. 5). The turntable is     tuned considering the desired targets, which are
automatically operated from the control room enabling a         previously calculated considering the potential boat
360° range of headings.                                         performance at different true wind speeds and yacht
                                                                courses. As previously said the velocity profile can be
3.1 Test arrangements and measurements setup
                                                                simulated by means of independent control of the
The large size of the low speed test section enables yacht      rotation speed of each fan joined to the traditional spires
models of quite large size to be used, so that the sails are    & roughness technique, while the twist can be simulated
large enough to be made using normal sail making                by twisting the flexible vanes by different amounts over

the height range. The wind tunnel speed is most usually        The photogrammetry based technique is relatively fast
limited by the strength of the model mast and rigging and      during the tunnel occupancy phase and in principle it
the power of the sheet winches.                                requires only three digital images be recorded from
Data acquisition can be performed in several ways: the         useful points. In order to overcome difficulties arising
usual procedure provides direct digital data acquisition       from sails overlapping especially in downwind
by means of National Instruments Data Acquisition              configurations and in order to be able to have at least
Boards (from 12 to 16 bits, from 8 differential channels       three useful points in each part of the sails the system is
up to 64 single-ended) and suitably written programs           equipped with eight cameras. For the present tests this
according to Matlab standards.                                 system is composed of five cameras, filming reflective
The data acquisition software calculates the forces and        targets placed on sails in sync, and a PC equipped with
moments using the dynamometer calibration matrix. The          acquiring and processing custom-made software.
forces are shown in the virtual panel designed on the          Cameras have resolution of 1392 x 1040 pixels,
computer screen in real time so that the sail trim can be      greyscale 1/2” CCD sensor, 17 fps (frames per second).
optimised because the effects of trimming the sails on the     Each of them mounts an optical zoom and a high
driving and heeling forces can be directly appreciated.        intensity infrared (830 nm) LED illuminator, triggered to
The model is set at an apparent wind angle and at a fixed      simultaneously flash with cameras frame rate. In order to
heel. After a sail trim has been explored, actual              reduce at the best cameras vibrations induced by the
measurements are obtained by sampling the data over a          wind, it was decided to fix cameras on photographic
period specified by the test manager (generally 30             heads constrained to the available stiffest points in the
seconds) with a sample frequency specified too. An             wind tunnel (fig.6).
important feature of wind testing procedure is that the
model should be easily visible during the tests so that the
sail tell-tales can be seen by the sail trimmer. For this
purposes some cameras placed in the wind tunnel as well
as onboard allow a view similar to the real life situation

Figure 4. Wind tunnel top and deck camera view during
testing                                                        Figure 6. Yacht model and cameras in the wind tunnel
                                                               High reflective markers are glued on 8 horizontal
In order to correlate force measurement readings and the       sections of each sail plus one on the top, on both
sail shape and in order to provide input data for CFD          windward and leeward side (fig 7).
calculations, an in-house photogrammetric measuring
system has been developed to recover flying shapes
during tests (fig.5).

                                                               Figure 7. Reflective markers on the main
                                                               Then, a custom-made software performs real time blob
                                                               detection and stores images sourced from cameras on a
                                                               hard disk.
Figure 5. Flying shape measurement system layout

As a result of this routine a table with the 2D blob         heeling angle, heeling force has to be reduced by the
detected coordinates is available for post process.          crew. The sail trimming routine adopted was to choose
                                                             the mainsail traveller position (initially quite high up to
                                                             windward) and then to vary the incidence and the twist of
                                                             the mainsail to power or de-power it, by over-trimming
                                                             or easing the main traveller and main sheet.
                                                             The genoa was initially trimmed in order to have the
                                                             maximum driving force condition and was fixed varying
                                                             the mainsail shape.
                                                             Once a specific trimming condition is obtained using the
                                                             real time force and moments values displayed by the data
                                                             acquisition system, a 30 seconds acquisition sampling
                                                             has been performed with 100Hz sample frequency, and
                                                             both time histories and mean values of each measured
                                                             quantity have been stored in a file.
                                                             The usual way of analysing data is to compare non
                                                             dimensional coefficients, allowing to compare the
                                                             efficiency of sails of different total area at different
                                                             conditions of dynamic pressure. The first analysis
                                                             performed is the variation of driving force coefficient Cx
                                                             with heeling force coefficient Cy. They are given by the
                                                                       Cx = 1
                                                                             2  Sv 2
                                                                       Cy =
Figure 8. Sails flying shape detection process                                1
                                                                              2    Sv 2                       (1)
Cameras have been previously calibrated using a custom       where
built calibration frame.                                        •     Fx is the driving force
The 3D marker points coordinate for each sail are then          •     Fy is the heeling force
obtained by means of a DLT (Direct Linear                       •     S is the actual sail area
Transformation) algorithm, reaching marker position             •     V is the wind speed
with an uncertainty equal to 0,5 mm.                            •       is air density
Marker coordinates are obtained as mean of their
position over a 20[sec] acquisition period with 17 Hz        As an example fig. 9 shows a comparative plot of Cx
acquisition rate.                                            versus Cy for the apparent wind angles tested. Each run
Then this 3D points array are used for surface modelling     (with its corresponding measured values) is shown for
as well as to extract the trim parameters as explained in    each AWA.

3.2 Upwind sails testing procedure

For each apparent wind angle tested the first task was to
reach the maximum driving force potentially achievable.
At the same time it was observed the influence of the
sails trimming changes using the data acquisition
program that visualizes the forces acting on yacht model
in real time.
Trimming the sails to obtain optimum sailing points
proved to be the most challenging task of the testing
Attempts were made to carry out the job as
systematically as possible. Firstly, the maximum drive
point was found by trimming the sails to the best using      Figure 9: Driving force coefficient vs heeling force
the cameras views, the tufts on the sails and the force      coefficient
measurements output data.
                                                             It can be seen that there are some sails settings at the
From there, the heeling force would be reduced to
                                                             highest values of heeling force coefficients where the
simulate the trim of the sails for windier conditions. In
                                                             driving force is lower than the maximum value. These
fact in real life windy conditions, to keep the optimum
                                                             non optimum values were obtained by oversheeting the

sails such that the mainsail generally had a tight leech
and the airflow separated in the head of the sail.
Therefore a selection was made to choose those points
that formed the envelope curves (maximum Cx for a
given Cy value) for each apparent wind angle (fig. 9).
Envelope curves have been drawn through the test points
with the greatest driving force at a given heeling force.
An example is reported in fig. 10.

                                                                Figure 11. Centre of effort height vs heeling force coefficient

Figure 10. Driving force coefficient envelope vs heeling
force coefficient
For the purpose of the analysis, in the following only
these points will be used.
The centre of effort height, Ceh, is obtained by dividing
the roll moment by the heeling force component in the
yacht body reference system:
          Ceh =
As an example, a plot of its variation with heeling force       Figure 12. Centre of effort longitudinal position vs heeling
for all angles can be seen in fig 11. Both all the measured     force coefficient
values and the envelope of the points corresponding to
maximum driving force at each heeling force are
reported. The results are given in terms of ratio between       3. SAILPLANS TESTED
centre of effort height from boat deck and mast height          According to the overall activities program 3 different
(P+BAS). The centre of effort longitudinal position, Cea,       main sails (with the same actual area but 3 different
is obtained by dividing the yaw moment by the heeling           roaches) named Mims, Mhr, and Mtri and 3 different jibs
force component in the yacht body reference system:             with different overlap (named G100, G135 and G150)
                  Mz                                            have been combined in a 92% fractionality
         Cea =                                                  configuration.. Note that the Mims mainsail has the IMS
                  Fy                                            maximum allowed roach without any penalty applied
As an example, a plot of its variation with heeling force       according to the IMS rule.
for all angles can be seen in fig 12. Both all the measured     Mainsail Roach level has been defined according to:
values and the envelope of the points corresponding to
maximum driving force at each heeling force are                                       AreaMain
reported. Cea is measured from the origin of the balance                  Roach =              1
(positive to bow) which is placed behind the mast.                                    P*E / 2                             (2)
The results are given in terms of ratio between centre of       Mainsails codes and dimensions are defined as follows:
effort longitudinal position from balance origin and yacht
model waterline length.                                                             Roach             P                E
It can be seen that Cea moves forward as Cy reduces.
                                                                Mims                0.193            1.94            0.637
This is explained by the way the sails are de-powered.
                                                                Mhr                 0.335            1.94            0.571
                                                                Mtri                0.096            1.94            0.695
                                                                                            Tab. 1

Jib codes are defined as follows:

 G100                                       100%
 G135                                       135%
 G150                                       150%
                          Tab. 2
All configurations were tested in upright condition and at
30° heeling too.
Only the IMS mainsail+135% jib have been tested at 15°
heeled condition too.
Table 3 summarises the situation.

                  Upright           Heel 15°         Heel 30°
Mims G100           X                                   X
Mims G135           X                  X                X
Mims G150           X                                   X
Mhr G100            X                                   X
Mtri G100           X                                   X
                          Tab. 3
Figures 13-17 show the different sailplans during the

                                                                 Figure 14. MtriG100 sailplan

                                                                 Figure 15. MimsG100 sailplan
                                                                 Apparent wind angles were chosen to be 22°, 27°, 32°
                                                                 and 42° which cover the upwind range.
                                                                 For each apparent wind angle, sail trimming during the
                                                                 wind tunnel tests were performed according to the
                                                                 abovementioned procedure. All the sails trimming have
                                                                 been performed by Gigio Russo of North Sails Italia
Figure 13. MhrG100 sailplan                                      using the remote control console for model winches. At
                                                                 the same time it was observed the influence of the sails
                                                                 trimming changes using the data acquisition program that
                                                                 visualizes the forces acting on yacht model in real time.

                                                                  •        Mx is the heeling moment
                                                                  •        S is the actual sail area
                                                                  •        Hmast is the mast height from the deck
                                                                  •        Va is apparent wind speed
                                                                  •          is air density

                                                        The apparent wind speed Va and apparent wind angle are
                                                        evaluated in the heeled plane perpendicular to the mast
                                                        according to:

                                                                             (                ) + (Vt sin                      )
                                                                                               2                                   2
                                                                  Va =             Vt cos                            cos
                                                                               V sin cos
                                                                   AWA = arctg t
                                                                                  Vt cos
                                                        where represent the true wind angle (yaw angle), Vt is
                                                        the wind tunnel flow velocity corresponding to the mean
                                                        dynamic pressure at each run and is the heel angle.
                                                        Figures 18-21 show test results relevant to the mainsail
                                                        medium roach and medium overlapping jib (MimsG135)
                                                        sailplan in terms of envelope curves (maximum Cx for a
                                                        given Cmx value) for each apparent wind angle.
                                                        In particular in each figure results are reported with
                                                        reference to each apparent wind angle tested in upright
                                                        and heeled condition too: in this case the resulting
                                                        apparent wind angle according to eqn. 4 is shown in the
Figure 16. MimsG150 salplan                             legend.
                                                                                   AWA 19.3 MimsG135
                                                                                   AWA 21.3 MimsG135
                                                                                   AWA 22 MimsG135

                                                         Cx [-]



                                                                     0.4     0.5       0.6    0.7        0.8     0.9       1             1.1    1.2    1.3
                                                                                                           CMx [-]

                                                        Figure 18. MimsG135 sailplan
Figure 17. MimsG135 sailplan
                                                                                    AWA 23.8 MimsG135
4. EXPERIMENTAL RESULTS                                           0.45
                                                                                    AWA 26.2 MimsG135
                                                                                    AWA 27 MimsG135

Using the aerodynamic driving force and aerodynamic
heeling moment Fx and CMx component in the yacht                   0.4

body reference system the corresponding coefficients
have been obtained as follows:
                                                         Cx [-]


     Cx =
          1                                                        0.3
             SVa2                            (3)
                Mx                                                0.25
     CM x =
               SH mastVa2                                          0.2
            2                                                        0.5      0.6       0.7        0.8      0.9        1               1.1     1.2     1.3
                                                                                                           CMx [-]
    • Fx is the driving force                           Figure 19. MimsG135 sailplan

          0.65                                                                                                        0.5
                           AWA 28.4 MimsG135                                                                                        AWA 23.8 MhrG100
            0.6            AWA 31.1 MimsG135                                                                                        AWA 27 MhrG100
                           AWA 32 MimsG135


 Cx [-]

                                                                                                            Cx [-]


            0.3                                                                                                       0.2

             0.5    0.6        0.7         0.8          0.9          1         1.1        1.2    1.3                    0.2     0.4          0.6         0.8             1       1.2         1.4     1.6
                                                       CMx [-]                                                                                                 CMx [-]

Figure 20. MimsG135 sailplan                                                                            Figure 23. MhrG100 sailplan

            0.9                                                                                                      0.65
                                                                                                                                      AWA 28.4 MhrG100
                          AWA 37.9 MimsG135
                                                                                                                      0.6             AWA 32 MhrG100
            0.8           AWA 41 MimsG135
                          AWA 42 MimsG135

            0.6                                                                                                      0.45
   Cx [-]

                                                                                                            Cx [-]

            0.5                                                                                                       0.4



            0.2                                                                                                       0.2
              0.4   0.5      0.6         0.7      0.8     0.9            1         1.1     1.2   1.3                    0.2     0.4          0.6         0.8             1       1.2         1.4     1.6
                                                    CMx [-]                                                                                                    CMx [-]

Figure 21. MimsG135 sailplan                                                                            Figure 24. MhrG100 sailplan
As can be seen the effect of heel is to reduce the
maximum driving force produced by sails at each                                                                                     AWA 37.9 MhrG100
apparent wind angle tested and this effect increases with                                                             0.7           AWA 42 MhrG100

the heeling angle increasing.                                                                                        0.65
The same situation has been found for each sailplan
tested: as an example figures 22-25 refer to max roach
mainsail with non overlapping jib (MhrG100).                                                                         0.55
                                                                                                            Cx [-]

          0.45                                                                                                        0.5

                          AWA 19.3 MhrG100
            0.4           AWA 22 MhrG100



                                                                                                                       0.4    0.5      0.6         0.7    0.8     0.9        1         1.1     1.2   1.3
 Cx [-]

                                                                                                                                                            CMx [-]

                                                                                                        Figure 25. MhrG100 sailplan
                                                                                                        Another interesting feature is that the reduction in
          0.15                                                                                          driving force is more evident in fully powered condition
                                                                                                        than in the depowered ones and this is a general trend for
              0.2     0.4          0.6           0.8             1           1.2         1.4     1.6    each sailplan tested.
                                                       CMx [-]
                                                                                                        With reference to the mainsail medium roach and
                                                                                                        medium overlapping jib (MimsG135) sailplan figure 26
Figure 22. MhrG100 sailplan
                                                                                                        shows the ratio between the driving force coefficient at
                                                                                                        different heel angle and the same quantity in upright
                                                                                                        condition for each apparent wind angle relevant to the

sailplan trim allowing for the maximum driving force.                 carried out and put in the numerical model of the wind
These ratio can be interpreted as a sort of efficiency                tunnel (figure 32). The boundary conditions were set to
parameter of the sailplan heeled condition.                           give a wind velocity profile similar to that in the wind
                                 Mims G135                                                        Mims G150

             1.05                                                                  1.2
              0.9                                       awa 22                      1                                    awa 22
  cx ratio

                                                                        cx ratio
             0.85                                       awa 27                                                           awa 27
              0.8                                       awa 32                                                           awa 32
             0.75                                       awa 42                     0.8                                   awa 42
              0.6                                                                  0.6
                        0   10       20       30   40                                    0   10      20        30   40
                                 heel [deg]                                                       heel [deg]

Figure 26. MimsG135 sailplan                                          Figure 29. MimsG150 sailplan
Figure 27 is relevant to heeling force coefficient ratio of
                                                                                                  Mhr G100
the same (MimsG135) sailplan.

                                                                                    1                                    awa 22
                                                                        cx ratio

                                                                                                                         awa 27
                1                                                                                                        awa 32
             0.95                                                                  0.8                                   awa 42
              0.9                                       awa 22
  cy ratio

             0.85                                       awa 27
              0.8                                       awa 32                     0.6
             0.75                                       awa 42                           0   10      20        30   40
                                                                                                  heel [deg]
                        0   10       20       30   40                 Figure 30. MhrG100 sailplan
                                 heel [deg]

                                                                                                  Mtri G100
Figure 27. MimsG135 sailplan
All the performed tests revealed a decrease in sailplan
driving force when the sailplan heels (figures 28-31).
                                                                                    1                                    awa 22
                                                                        cx ratio

                                                                                                                         awa 27
                                                                                                                         awa 32
                                 Mims G100
                                                                                   0.8                                   awa 42

                                                        awa 22                           0   10      20        30   40
  cx ratio

                                                        awa 27                                    heel [deg]
                                                        awa 32
             0.8                                        awa 42
                                                                      Figure 31. MtriG100 sailplan

                    0       10      20        30   40
                                 heel [deg]

Figure 28. MimsG100 sailplan
In order to gain further understanding of the sailplans
aerodynamic      behaviour    experimentally     outlined
numerical simulations have been carried out using RANS
methods. In particular numerical simulations have been
performed by means of FLUENT CFD code with the
realizable k- turbulence model. A numerical model of
each tested sailplan including hull and rigging has been              Figure 32. Wind tunnel and yacht numerical model

In the following, for lack of space, results concerning        on the sailplan windward side; moreover in the lower
only the medium roach mainsail with non overlapping jib        part of the jib pressure increases with heel reducing the
(MimsG100) will be reported.                                   suction on the leeward side.
Fig. 33 shows numerical model of sails including yacht         In order to understand this behaviour it’s useful to refer
hull, which has been used to simulate yacht upwind             to figures 41-42 which show the flow velocity vectors
behaviour at different heel angles (sailing upright,           coloured by magnitude (normalised to the free stream
15°heeled and 30° heeled) .                                    incoming flow) in a plane perpendicular to the mast at
Numerical simulation have been performed at 22°                25% of mast height from the deck respectively for
apparent wind angle and for each of the heel angle             upright, 15°heeled and 30° heeled conditions.
considered the flying shape corresponding to maximum
drive condition trimming at different heel angle has been
used in order to generate the numerical mesh.

                                                               Figure 35. Leeward Cp contours at 15° heel

Figure 33. MimsG100 sailplan numerical model
Figures 34-35-36 show the MimsG100 sailplan leeward
side pressure coefficient contour respectively for upright,
15°heeled and 30° heeled condition concerning 22°
apparent wind angle close hauled sailing condition
                                                               Figure 36. Leeward Cp contours at 30° heel

Figure 31. Leeward Cp contours in upright condition
As can be seen heel increasing result in a less of a           Figure 37. Windward Cp contours in upright condition
pressure drop on both the sails, due to pressure decrease

                                                                   stated by the heeled plane model described in the next

Figure 38. Windward Cp contours at 15° heel

                                                                   Figure 41. Velocity vectors in a plane perpendicular to the
                                                                   mast (25% mast height ) at 15° heel

Figure 39. Windward Cp contours at 30° heel
When the yacht heels flow angle of attack reduces and
the corresponding lift decreases, leading to a reduction
of the driving force too. As can be seen upright condition
is associated to some separation on the jib leeward side
which disappears at higher heel angles, leading to a lift          Figure 42. Velocity vectors in a plane perpendicular to the
reduction too.                                                     mast (25% mast height ) at 30° heel

                                                                   5. AERO MODELLING AND HEELED PLANE
                                                                      APPROACH: SOME CONSIDERATIONS
                                                                   Since 1978 when the first velocity prediction programs
                                                                   for yachts was officially introduced for rating purposes
                                                                   the problem of modelling sail forces is a fundamental
                                                                   With reference to most of up to date available VPPs it
                                                                   can be said that aerodynamic model is mainly derived
                                                                   from the first aerodynamic model well known as Kerwin
                                                                   model [3].
                                                                   Many principles of the aerodynamics of sails can be
                                                                   taken from the thin airfoil theory even if significant
                                                                   differences can be found: in a similar way to a wing
Figure 40. Velocity vectors in a plane perpendicular to the        yacht sails are lifting bodies where due to their shapes
mast (25% mast height ) in upright condition                       and the direction of the onset flow circulation appears
                                                                   increasing fluid velocity on the leeward side and
This flow behaviour around the sails confirms also the             decreasing velocity in the windward side with a
apparent wind angle reduction associated to heeling as

consequent high pressure region on the windward side             In particular for each test performed (as indicated on the
and low-pressure region on the leeward side.                     abscissa axis named “prove” in fig. 44) the 3 component
The lift and drag forces, resulting from the pressure            of the aerodynamic measured force are reported.
regions around the sails can be expressed in terms of                                    Zloc

non-dimensional coefficients so that any forces and
moments can be evaluated considering actual sail area
and dynamic pressure of the free stream onset speed of
the flow.
With reference to a wing the lift and drag coefficients are
primarily a function of the angle of attack: on a sailing                                                       Xloc = Xbil
yacht this quantity is not easy to be defined due to
continuous sails shape changing due to sails trimming.                                                   Yloc
Hence in case of sails the angle of attack concept is
replaced by the apparent wind angle which is the angle                                                 Ybil
between the relative free-stream onset flow and the yacht
centreline.                                                                                     Zbil
Moreover the free-stream speed of the onset flow to be
used in evaluate the dynamic pressure is usually                 Figure 43. Balance and boat reference systems
considered to be the apparent wind speed.                        With reference to fig. 44 blue symbols are relevant to
Wind tunnel tests and full scale experiments are the most        balance axes aerodynamic force components (named
suitable way to evaluate the drag and lift coefficients of       “bil”) while red symbols are relevant to the boat
the sailplan for different apparent wind angles                  reference system values (named “loc”) defined in fig. 43.
considering the sails geometry, the relative direction of        More in details in figure 44:
the onset flow, the flow structure (gradient and twist) and
the trim of the sails.
                                                                     •    Runs 1-16 are 22° AWA and 30° heel tests
A typical representation of forces acting on the sailplan
                                                                     •    Runs 17-28 are 27° AWA and 30° heel tests
are based on lift and drag sailplan coefficients plotted
against the apparent wind angle.                                     •    Runs 29-42 are 32° AWA and 30° heel tests
The effect of heel is generally taken into account using             •    Runs 43-62 are 22° AWA and 30° heel tests
the so called effective angle theory [Jackson, Campbell]             •    Runs 63-95 are 42° AWA and upright tests
which is used to address the fact that the heel angle                •    Runs 96-109 are 32° AWA and upright tests
influences the flow around the sails since the onset flow            •    Runs 110-122 are 27° AWA and upright tests
can always been considered as being horizontal. As the               •    Runs 123-136 are 22° AWA and upright tests
yacht heels the onset flow is not longer perpendicular to
the leading edge of the sails and due this the resulting lift    As can be seen the aerodynamic force component along
and drag forces are different for each heel angle.               the mast (“zloc” component) is quite zero except for the
Each aero model must take into account for the fact that         42°AWA runs: this was a systematic effects shown by
lift and drag coefficients are no only a function of the         tests with each sailplan tested.
apparent wind angle but also of the yacht heel.
Kerwin [3] and the so called effective angle theory
assume that the sails are insensitive to the flow
component along their span (i.e. along the mast) and that
only the flow component perpendicular to the mast
produces the lift and drag forces.
This represents one of the tougher issue of upwind
aerodynamics and some discussions have been found in
literature also very recently [Jackson 2001], [Teeters Sea
Aim of this paragraph is to discuss the appropriateness of
this assumption and to investigate in more details its
consequences on results available from aero models
based on this underlying hypothesis.
More in details the flow component along the chord of
the sails can be seen as the flow component in the heeled
plane, which is a plane perpendicular to the mast and this
means that the sails are insensitive to the flow component       Figure 44. MimsG100 runs sequence
along the mast.                                                  Experimental measures demonstrate that Kerwin
As an example in fig. 44 all tests performed by the              assumption that the sails are insensitive to the flow
authors for MimsG100 sail plan are reported (136 runs).          component along the mast is substantially verified.

Coming back to the “heeled plane” model, the flow
component in the heeled plane is called the effective flow
and is defined by the effective angle and effective speed
according to the following equations:

                (            ) + (Vt sin         )
                             2                       2
         Va =       Vt cos                 cos
                     V sin cos
         AWA = arctg t
                        Vt cos

where represent the true wind angle (yaw angle), Vt is
the true wind speed and is the heel angle.
Using the driving and heeling aerodynamic force Fx and
Fy component in the yacht body reference system the
corresponding drag and lift forces components can be
obtained as follows:
                                                                    Figure 46. Lift coefficient vs apparent wind angle
         DRAG = Fx cos( AWA) + Fy sin( AWA)
                                                         (6)        Heel effect on sails aerodynamics is outlined in the
         LIFT = Fx sin( AWA) + Fy cos( AWA)                         following: in figures 43-44 the measured CD and CL
                                                                    values defined using the effective wind angle and
                                                                    effective wind speed according to eq.(5) are reported for
Then the corresponding drag and lift coefficients CD and
                                                                    the 30° heel condition too.
CL can be evaluated:

         DRAG =        Va2C D ( AWA) S
                     2                                   (7)
         LIFT =       Va2C L ( AWA) S

where S is the actual sailplan area.
So when the boat heels over the apparent wind angle
decreases and the apparent wind speed reduces and this
results in a loss of aerodynamic drive force.
This approach is very interesting because only one set of
sails coefficients can be used to any heel angle.
As an example in figures 45-46 the CD and CL measured
values at different AWA are reported for the medium
roach mainsail+ non overlapping jib in upright condition.
                                                                    Figure 47. MimsG100 drag coefficient
At each AWA, values corresponding to each run (i.e.
each trim) performed are reported and red full dots
correspond to the maximum driving force condition
trimming point.

                                                                    Figure 48. MimsG100 lift coefficient
                                                                    Figures 49-50 refer to the medium roach + medium
                                                                    overlapping sailplan where upright, 15° heel and 30° heel
Figure 45. Drag coefficient vs apparent wind angle                  configuration are reported.

                                                                yacht heel and on the actual apparent wind angle,
                                                                obtained from an interpolation between the available
                                                                experimental database.


                                                                         0.5                                          heel 0

                                                                         0.4                                          heel 15
                                                                         0.3                                          heel 30
                                                                               0   10   20             30   40   50
                                                                                             Awa [°]

Figure 49. MimsG135 drag coefficient
                                                                Figure 51. MimsG135 driving force coefficient


                                                                           1                                          heel 0

                                                                         0.8                                          heel 15
                                                                         0.6                                          heel 30
                                                                               0   10   20             30   40   50
                                                                                             Awa [°]

                                                                Figure 52. MimsG135 heeling force coefficient
Figure 50. MimsG135 lift coefficient
As a general comment from the experimental obtained             Finally it’s also interesting to mention that results and
result it can be seen that CD and CL curves tend to be          conclusion of the present paper go exactly in the opposite
different with respect to AWA at different heels and            direction with respect of results presented in [8]. Despite
differences are larger at wider apparent wind angles.           that only qualitative results are reported in that paper
This trend is confirmed also for all the other sailplan         without any details on the sailplan tested available, it’s
tested (not reported here for lack of space reasons).           author’s opinion that in principle results showing that
It should be also noticed that using the so called effective    there is no drop-off in driving force over the entire
angle approach implies to move to any heel angle on the         operational range of the sails until 30° heel are not
upright condition coefficients curves, depending on the         particularly surprising and can be explained considering
effective wind angle, leading to a general lift and drag        sails-hull interaction effects. Some wind tunnel tests
overestimation at wider angles while at the closer angles       recently performed by the authors on a IACC Version 5
this error is going to reduce.                                  yacht model on upwind sails at various heel angles (not
The corresponding situation for the abovementioned              reported here for confidentiality reasons) reveal that at
sailplan in terms of drive and heeling force is outlined in     20° heel the effect of heel was to produce low base drag
figures 51-52.                                                  compared to other heel and associated higher driving
As can be seen at wider apparent wind angle using               force but that could be attributed to changes in the
upright condition coefficients and effective wind angle         windage drag with heel: this moreover offers the
both forces are overestimated.                                  prospect of investigating this feature together with hull
This could also explain the reason why VPP solutions are        shape to reduce windage at different heel angles
generally obtained in association with large values of flat     Another important point outlined from author’s
parameter: in fact depowering introduced by flat values         performed tests and affecting aerodynamic forces with
sometime less than 0.5-0.6 are not realistic and probably       heel was related to the boom height with respect to the
due to overestimation of aerodynamic forces in heeled           deck: figure 53-54 show the wind velocity vectors
conditions.                                                     coloured by normalisation to the free stream incoming
An approach more consistent with experimental data              flow in a vertical transverse plane that cuts the mainsail
could be to use CD and CL values, depending on actual           at 33% of boom length (from the mast) respectively for

upright, 15°heeled and 30° heeled conditions obtained          6. CONCLUSIONS
from the abovementioned numerical simulations.
                                                               This paper gives an overview of the large amount of
                                                               research activities carried out at Politecnico di Milano
                                                               Twisted Flow Wind Tunnel in order to investigate the
                                                               performance of upwind sails in heeled condition. Several
                                                               rig planform variations in mainsail roach and jib overlap
                                                               have been tested. Experimental results show that sailplan
                                                               aerodynamic forces reduce with heeling, that drag and
                                                               lift coefficients curves are different with respect to
                                                               apparent wind angle at different heels and differences are
                                                               larger at wider apparent wind angles.
                                                               This trend is confirmed for all the sailplan tested and has
                                                               been clarified with the aid of numerical results obtained
                                                               using RANS methods performed on the tested sailplan
                                                               Experimental results reveal that to the so called “heeled
                                                               plane approach”, largely used in the standard VPP
Figure 53. Velocity vectors in a vertical plane                aerodynamic models, leads to a general lift and drag
perpendicular to the boom in upright condition                 overestimation at wider angles while at the closer angles
                                                               this error is going to reduce. Main conclusion is that with
                                                               reference to standard applications the so called heeled
                                                               plane approach is quite adequate even if at upwind wider
                                                               apparent wind angle both forces are overestimated.
                                                               Potential improvement of the generally used Kerwin’s
                                                               assumptions based aerodynamic model, in order to take
                                                               into account heel effects, are finally outlined based on
                                                               the available experimental database.

                                                               1.   J. M. C. Campbell, & A. R. Claughton – Wind
                                                                    Tunnel Testing of Sailing Yacht Rigs – 13th HISVA
                                                                    symposium – Amsterdam 1994
                                                               2.   Fossati F. et al., ‘Wind Tunnel Techniques for
                                                                    Investigation and Optimization of Sailing Yachts
Figure 54. Velocity vectors in a vertical plane
perpendicular to the boom at 15° heel
                                                                    Aerodynamics’, High Performance Yacht Design
                                                                    Conference Auckland, 14-16-Feb. 2006
                                                               3.   Kerwin, JE “A velocity Prediction Program for
                                                                    Ocean racing yachts”, Rep 78-11 MIT, July 1978
                                                               4.   Fossati, F.& Zasso, A.& Viola I., “Twisted Flow
                                                                    Wind Tunnel Design for Yacht Aerodynamic
                                                                    Studies”, Proc. of the 4th European and African
                                                                    Conference on Wind Engineering, J. Naprstek & C.
                                                                    Fisher, Prague, 11-15 July, 2005.
                                                               5.   Fossati F. et al, “Experimental Database of Sails
                                                                    Performance and Flying Shapes in Upwind
                                                                    Conditions” Innov’sail 2008, RINA 29-30 May
                                                                    Lorient, 2008
                                                               6.   P. S. Jackson, “Modelling the Aerodynamics of
                                                                    Upwind Sails” – Journal of Wind Eng. & Ind.
Figure 55. Velocity vectors in a vertical plane                     Aerodyn., vol. 63 , 1996
perpendicular to the boom at 30° heel
                                                               7.   P. S. Jackson, “An improved Upwind Sail Model for
These figures show that a vortex generated by deck edge
which increases with heel, but that doesn’t affect                  VPPs” – SNAME 15th CSYS, Annapolis, 2001
substantially the flow under the boom: this leads to the       8.   Teeters J., “The Story so Far”, SeaHorse Magazine,
angle of attack reduction associated to heel increasing the         July 2007
main reason in decreasing sailplan developed forces.


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